
Calculus of Variations on Fibred Manifolds and Variational Physics
Description
Alles über E-Books | Antworten auf Fragen rund um E-Books, Kopierschutz und Dateiformate finden Sie in unserem Info- & Hilfebereich.
This book presents modern variational calculus in mechanics and field theories with applications to theoretical physics. It is based on modern mathematical tools, specifically fibred spaces and their jet prolongations, which operate with vector fields and differential forms on foundational structures. The book systematically explains Lagrangian and Hamiltonian mechanics and field theory, with a focused exploration of the underlying structures. Additionally, it addresses the well-known inverse problem of calculus of variations and provides examples illustrating key variational physical theories.
The text is complemented by solved examples from physics and includes exercises designed to help readers master the subject. Aimed at PhD students, postdocs, and interested researchers, this book assumes prior knowledge of mathematical analysis, linear and multilinear algebra, as well as elements of general and theoretical physics for effective engagement with the discussion.
More details
Other editions
Additional editions

Persons
Jana Musilová is a full Professor of General Physics and Mathematical Physics at the Institute of Theoretical Physics and Astrophysics at the Faculty of Science, Masaryk University. She obtained her PhD (CSc) in Experimental Physics from Masaryk University in 1980. In 1991, she completed her habilitation in Solid State Physics and Acoustics, also at Masaryk University.Her research interests have included slow electron diffraction, modulation techniques for studying the optical properties of semiconductors, and ongoing research in the field of calculus of variations (nonholonomic mechanics), geometric analysis, and mathematical physics.She is also actively engaged in research in the field of physics education, teaching basic and advanced courses in physics and mathematics at Masaryk University.
Pavla Musilová is an Assistant Professor at the Institute of Theoretical Physics and Astrophysics at the Faculty of Science, Masaryk University. She obtained her Master's degrees in Physics, Teaching Physics and Mathematics, and in Mathematics - Algebra and Geometry from Masaryk University in 1999 and 2019, respectively. In 2002, she successfully completed her PhD studies in Theoretical Physics at Masaryk University.Her research is devoted to problems of natural operators on manifolds, pseudoriemannian geometries, and physics education. At the Faculty of Science of Masaryk University, her teaching is focused on courses in mathematical analysis, linear algebra and geometry, multilinear algebra, and differential and integral calculus of forms on manifolds.
Olga Rossi , formerly Krupková (┼ 2019), was a full Professor of Mathematics and head of the Department of Mathematics at the Faculty of Sciences of the University of Ostrava. She completed her Master's degree and PhD studies in Theoretical Physics at Charles University in Prague. She worked at the Silesian University in Opava, Palacký University in Olomouc, and, in her later years, at the University of Ostrava. Additionally, she held positions at renowned universities worldwide, including Gent, La Trobe University Melbourne, and Stockholm.Professor Rossi served as the EWM regional coordinator for the Czech Republic and was a member of the EWM-WIM Committee of the European Mathematical Society.Her research focused on global analysis and geometry, geometric mechanics, and geometry and mathematical physics. She continues to be recognized by the global mathematical and physical community as an important expert in her fields of research.
Content
Chapter 1. Introduction.- Chapter 2. Fibred manifolds.- Chapter 3. Vector fields and differential forms.- Chapter 4. Calculus of variations.- Chapter 5. Dynamical forms and the inverse problem.- Chapter 6. Hamiltonian systems.- Chapter 7. Elements of the variational sequences.- Chapter 8. Extension: Geometrical structures for field theories.- Chapter 9. Variational physics.- Chapter 10. Appendix.
System requirements
File format: PDF
Copy protection: Watermark-DRM (Digital Rights Management)
System requirements:
- Computer (Windows; MacOS X; Linux): Use the free software Adobe Reader, Adobe Digital Editions, or any other PDF viewer of your choice (see eBook Help).
- Tablet/Smartphone (Android; iOS): Install the free app Adobe Digital Editions or another reading app for eBooks, e.g., PocketBook (see eBook Help).
- E-reader: Bookeen, Kobo, Pocketbook, Sony, Tolino and many more (only limited: Kindle).
The file format PDF always displays a book page identically on any hardware. This makes PDF suitable for complex layouts such as those used in textbooks and reference books (images, tables, columns, footnotes). Unfortunately, on the small screens of e-readers or smartphones, PDFs are rather annoying, requiring too much scrolling.
This eBook uses Watermark-DRM, a „soft” copy protection. This means that there are no technical restrictions to prevent illegal distribution. However, there is a personalised watermark embedded in the eBook that can be used to identify the purchaser of the eBook in the event of misuse and to provide evidence for legal purposes.
For more information, see our eBook Help page.